I wrote a (very long) blog post about those viral math problems and am looking for feedback, especially from people who are not convinced that the problem is ambiguous.
It's about a 30min read so thank you in advance if you really take the time to read it, but I think it's worth it if you joined such discussions in the past, but I'm probably biased because I wrote it :)
My only complaint is the suggestion that engineers like to be clear. My undergrad classes included far too many things like 2 cos 2 x sin y
I'd say engineers like to be exact, but they like being lazy even more
Having read your article, I contend it should be:
P(arentheses)
E(xponents)
M(ultiplication)D(ivision)
A(ddition)S(ubtraction)
and strong juxtaposition should be thrown out the window.
Why? Well, to be clear, I would prefer one of them die so we can get past this argument that pops up every few years so weak or strong doesn't matter much to me, and I think weak juxtaposition is more easily taught and more easily supported by PEMDAS. I'm not saying it receives direct support, but rather the lack of instruction has us fall back on what we know as an overarching rule (multiplication and division are equal). Strong juxtaposition has an additional ruling to PEMDAS that specifies this specific case, whereas weak juxtaposition doesn't need an additional ruling (and I would argue anyone who says otherwise isn't logically extrapolating from the PEMDAS ruleset). I don't think the sides are as equal as people pose.
To note, yes, PEMDAS is a teaching tool and yes there are obviously other ways of thinking of math. But do those matter? The mathematical system we currently use will work for any usecase it does currently regardless of the juxtaposition we pick, brackets/parentheses (as well as better ordering of operations when writing them down) can pick up any slack. Weak juxtaposition provides better benefits because it has less rules (and is thusly simpler).
But again, I really don't care. Just let one die. Kill it, if you have to.
You guys are doing it all wrong: ask chatgpt for the correct answer and paste it here. Done.
Who needs to learn or know anything really?
I don't remember everything, but I remember the first two operations are exponents then parentheses. Edit: wait is it the other way around?
Meanwhile, I'm over in the corner like 
Hi, I’m stupid, is it 1+2 first, then multiple it by 2, then divide 6 by 6?
Or is it 1+2, then divide 6 by 2, then multiple?
I think it’s the first one but I’ve got no idea.
You lost me on the section when you started going into different calculators, but I read the rest of the post. Well written even if I ultimately disagree!
The reason imo there is ambiguity with these math problems is bad/outdated teaching. The way I was taught pemdas, you always do the left-most operations first, while otherwise still following the ordering.
Doing this for 6÷2(1+2), there is no ambiguity that the answer is 9. You do your parentheses first as always, 6÷2(3), and then since division and multiplication are equal in ordering weight, you do the division first because it's the left most operation, leaving us 3(3), which is of course 9.
If someone wrote this equation with the intention that the answer is 1, they wrote the equation wrong, simple as that.
There has apparently been historical disagreement over whether 6÷2(3) is equivalent to 6÷2x3
As a logician instead of a mathemetician, the answer is "they're both wrong because they have proven themselves ambiguous". Of course, my answer would be RPN to be a jerk or just have more parens to be a programmer
My years out of school has made me forget about how division notation is actually supposed to work and how genuinely useless the ÷ and / symbols are outside the most basic two-number problems. And it's entirely me being dumb because I've already written problems as 6÷(2(1+2)) to account for it before. Me brain dun work right ;~;
There's no forms consensus on which one is correct. To avoid misunderstanding mathematicians use a horizontal bar.
The ambiguous ones at least have some discussion around it. The ones I've seen thenxouple times I had the misfortune of seeing them on Facebook were just straight up basic order of operations questions. They weren't ambiguous, they were about a 4th grade math level, and all thenpeople from my high-school that complain that school never taught them anything were completely failing to get it.
I'm talking like 4+1x2 and a bunch of people were saying it was 10.
Forgot the algebra using fruit emoji or whatever the fuck.
Bonus points for the stuff where suddenly one of the symbols has changed and it's "supposedly" 1/2 or 2/3 etc. of a banana now, without that symbol having been defined.
When I used to play WoW years ago I'd always put -6 x 6 - 6 = -12 in trade chat and they would all lose their minds.
Adding that incorrect solution usually got them more riled up than having no solution.
I found a few typos. In the 2nd paragraph under the section "strong feelings", you use "than" when it should be "then". More importantly, when talking about distributive properties, you say x(x+z)=xy+xz. I believe you meant x(y+z)=xy+xz.
Otherwise, I enjoyed that read. I'm embarrassed to say that I did think pemdas meant multiplication came before division, however I'm proud to say that I've unconsciously known that it's important to avoid the ambiguity by putting parentheses everywhere for example when I make formulas in spreadsheets. Which by the way, spreadsheets generally allow multiplication by juxtaposition.
I guess if you wrote it out with a different annotation it would be
-‐--------‐--------------
=
-‐--------‐--------------
=
--‐--------‐--------------
=1
I hate the stupid things though
I recall learning in school that it should be left to right when in doubt. Probably a cop-out from the teacher
I just finished your article and wow! I'm definitely going to save it and share it the next time I come across another one of those viral problems. It was incredibly thorough and well researched, you clearly put a lot of energy and effort into it and it blew me away. It was really refreshing to see someone articulate themselves so passionately with supporting research. I look forward to reading more of your work!! 👏
A fair criticism. Though I think the hating on PEDMAS (or BODMAS as I was taught) is pretty harsh, as it very much does represent parts of the standard of reading mathematical notation when taught correctly. At least I personally was taught its true form was a vertical format:
B
O
DM
AS
I'd also say it's problematic to rely on calculators to implement or demonstrate standards, they do have their own issues.
But overall, hey, it's cool. The world needs more passionate criticisms of ambiguous communication turning into a massive interpration A vs interpretation B argument rather than admitting "maybe it's just ambiguous".
I feel like if a blog post presents 2 options and labels one as the "scientific" one... And it is a deserved Label. Then there is probably a easy case to be made that we should teach children how to understand scientific papers and solve the equation in it themselves.
Honestly I feel like it reads better too but that is just me